Weighted-average life

In <a href="/facts/Finance/fLh1GgN8">finance</a>, the weighted-average life (WAL) of an <a href="/facts/Amortizing_loan/V9JzbYlG">amortizing loan</a> or amortizing bond, also called average life, is the <a href="/facts/Weighted_average/VHyJfPxb">weighted average</a> of the times of the principal repayments: it's the average time until a dollar of principal is repaid.
In a formula,

WAL
        
        =
        
          ∑
          
            i
            =
            1
          
          
            n
          
        
        
          
            
              P
              
                i
              
            
            P
          
        
        
          t
          
            i
          
        
        ,
      
    
    {\displaystyle {\text{WAL}}=\sum _{i=1}^{n}{\frac {P_{i}}{P}}t_{i},}

where:

<ul><li>
 
 
 
 P
 
 
 {\displaystyle P}
 
 is the (total) principal,</li>
<li>
 
 
 
 
 P
 
 i
 
 
 
 
 {\displaystyle P_{i}}
 
 is the principal repayment that is included in payment 
 
 
 
 i
 
 
 {\displaystyle i}
 
, hence</li>
<li>
 
 
 
 
 
 
 P
 
 i
 
 
 P
 
 
 
 
 {\displaystyle {\frac {P_{i}}{P}}}
 
 is the fraction of the total principal that is included in payment 
 
 
 
 i
 
 
 {\displaystyle i}
 
, and</li>
<li>
 
 
 
 
 t
 
 i
 
 
 
 
 {\displaystyle t_{i}}
 
 is the time (in years) from the calculation date to payment 
 
 
 
 i
 
 
 {\displaystyle i}
 
.</li></ul>
If desired, 
 
 
 
 
 t
 
 i
 
 
 
 
 {\displaystyle t_{i}}
 
 can be expanded as 
 
 
 
 
 
 1
 12
 
 
 (
 i
 +
 α
 −
 1
 )
 
 
 {\displaystyle {\frac {1}{12}}(i+\alpha -1)}
 
 for a monthly bond, where 
 
 
 
 α
 
 
 {\displaystyle \alpha }
 
 is the fraction of a month between <a href="/facts/Settlement_date/wVeoqotT">settlement date</a> and first cash flow date.

Weighted-average life open-in-new

Weighted-average life